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Testing and numerical modelling of lean duplex stainless steel

hollow section columns

M. Theofanous and L. Gardner

Abstract

Stainless steels are employed in a wide range of structural applications. The austenitic grades,

particularly EN 1.4301 and EN 1.4401 and their low-carbon variants EN 1.4307 and EN

1.4404 are the most commonly used within construction and these typically contain around 8-

11% nickel. The nickel represents a large portion of the total material cost and thus high

nickel prices and price volatility have a strong bearing on both the cost and price stability of

stainless steel. While austenitic stainless steel remains the most favourable material choice in

many applications, greater emphasis is now being placed on the development of alternative

grades with lower nickel content. In this study, the material behaviour and compressive

structural response of a lean duplex stainless steel (EN 1.4162), which contains approximately

1.5% nickel are examined. A total of eight stub column tests and twelve long column tests on

lean duplex stainless steel square (SHS) and rectangular hollow sections (RHS) are reported.

Precise measurements of material and geometric properties of the test specimens were also

made, including the assessment of local and global geometric imperfections. The

experimental studies were supplemented by finite element analysis and parametric studies

were performed to generate results over a wider range of cross-sectional and member

slenderness. Both the experimental and numerical results were used to assess the applicability

of the Eurocode 3: Part 1-4 provisions regarding the Class 3 slenderness limit and effective

width formula for internal elements in compression and the column buckling curve for hollow

sections to lean duplex structural components. Comparisons between the structural

performance of lean duplex stainless steel and that of other more commonly used stainless

steel grades are also presented, showing lean duplex to be an attractive choice for structural

applications.

* ManuscriptClick here to view linked References

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Keywords: Buckling, Classification, Columns, Experiments, Finite element, Hollow section,

Lean Duplex, Numerical modelling, Stainless steel, Stub columns.

1. Introduction

There is a wide variety of grades of stainless steels, providing a range of material

characteristics to suit the demands of numerous, diverse engineering applications. Both

overall, and within the construction industry, the austenitic grades feature most prominently

[1]. The most commonly employed grades of austenitic stainless steel are EN 1.4301/1.4307

and EN 1.4401/1.4404, which contain around 8-11% nickel [2]. Nickel stabilises the

austenitic microstructure and therefore contributes to the associated favourable characteristics

such as formability, weldability, toughness and high temperature properties. However, nickel

also represents a significant portion of the cost of austenitic stainless steel and this has led,

particularly in recent years to the development and evaluation of alternative grades of

stainless steel with low nickel content.

Appropriate material selection, taking due account of in-service performance, economics and

environmental conditions, involves matching the material characteristics to the particular

demands of the application. Within construction, although austenitic stainless steels are the

most widely specified, their strengths are often not fully utilised; a recently developed ‘lean

duplex’ stainless steel, containing approximately 1.5% nickel, may offer a more appropriate

balance of properties for structural applications. The particular grade considered in this study

is EN 1.4162, which is generally less expensive and possesses higher strength than the

familiar austenitics, while still retaining good corrosion resistance and high temperature

properties [3], together with adequate weldability [4] and fracture toughness [5]. Examples of

the use of lean duplex stainless steel in construction have already emerged [6], including

footbridges in FÖrde, Norway and Siena, Italy; the latter is shown in Fig. 1.

Despite early applications of lean duplex stainless steel, its structural properties remain

largely unverified as no test data on structural components have been reported to date. A

research project is underway at Imperial College London to address these shortcomings,

focusing initially on cold-formed hollow sections. Material properties derived from tensile

and compressive coupon tests, slenderness limits for cross-section classification and effective

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width formulae for slender sections have been recently developed by the authors [7]. This

paper examines the compressive behaviour of lean duplex stainless steel square and

rectangular hollow sections (SHS and RHS respectively). Eight stub column tests and twelve

flexural buckling tests have been carried out and are reported in detail herein. The test results

were used to validate finite element (FE) models, which were thereafter employed in

parametric studies, to expand the range of available structural performance data, studying the

influence, in particular, of cross-section and member slenderness. Both the experimental and

numerical results were used to assess the applicability of the European structural design

provisions for stainless steel EN 1993-1-4 [8] to lean duplex stainless steel structural

components. Comparisons with recent proposals made by the authors regarding the

classification of stainless steel cross-sections [9], as well as comparisons with the structural

performance of other commonly used structural stainless steel grades are also included.

2. Experimental investigation

2.1 Introduction

An experimental investigation into the structural performance of lean duplex stainless steel

(grade EN 1.4162) SHS and RHS was conducted in the Structures Laboratory at Imperial

College London. The laboratory testing program comprised tensile and compressive tests on

flat coupons and tensile tests on corner coupons extracted from the cold-formed sections,

eight three-point bending tests, eight stub column tests and twelve flexural buckling tests. The

chemical composition of the tested material as given in the mill certificates is displayed in

Table 1. A detailed description of the experimental set-up and the experimental results of the

material tests and three-point bending tests is given in [7], whereas the stub column tests and

flexural buckling tests are reported in detail in this section.

2.2 Material properties

The material properties derived from the coupon tests, which are used in the assessment of the

member test results and the development of the FE models are given in Tables 2-4 for tensile

flat, compressive flat and tensile corner material, respectively. The reported material

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parameters are the Young’s modulus E, the 0.2% and 1% proof stresses σ0.2 and σ1.0,

respectively, the ultimate tensile stress σu, the plastic strain at fracture εf (based on elongation

over the standard gauge length A65.5 , where A is the cross-sectional area of the coupon),

and the strain hardening exponents n and n’0.2,1.0 used in the compound Ramberg-Osgood

material model [10-13], which is a two-stage version of the basic Ramberg-Osgood model

[14, 15]. The key minimum specified material properties for grade EN 1.4162 stainless steel

cold-rolled strip, as defined in [16], and included in EN 10088-4 [2], are as follows: σ0.2=530

N/mm2, σu=700-900 N/mm2, εf=30% (over a gauge length A65.5 ).

2.3 Stub column tests

Four section sizes were employed for the stub column tests, namely SHS 100×100×4, SHS

80×80×4, SHS 60×60×3 and RHS 80×40×4. Two repeated concentric compression tests were

carried out for each of the cross-section sizes to enable the determination of a suitable Class 3

limit for lean duplex stainless steel internal elements in compression. All specimens were

cold-rolled and seam welded. A stub column length equal to four times its mean nominal

cross-sectional width was chosen, which is deemed long enough to include a representative

pattern of residual stresses and geometric imperfections, yet short enough to avoid overall

flexural buckling [17].

Measurements of the basic geometry and initial geometric imperfections of the specimens

were conducted prior to testing. The geometric imperfections measurements followed the

procedure reported by Schafer and Peköz in [18]. Local geometric imperfections were

measured only over the middle half of each specimen’s length in order to eliminate the effect

of end flaring, which results from the release of residual stresses following cutting operations

[19]. The same approach has been successfully adopted in previous studies [20, 21]. The

maximum measured local geometric imperfection w0 for each nominal stub column

dimension is given in Table 5. Table 5 also includes the measured geometry (see Fig. 2) of

each stub column specimen, where L is the stub column length, B is the section width, H is

the section depth, t is the thickness and ri is the internal corner radius.

The ends of the stub columns were milled flat and square and were compressed between

parallel plattens in a self contained 300 T Amsler hydraulic testing machine as depicted in

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Fig. 3. The instrumentation consisted of four LVDTs to measure the end shortening between

the flat plattens, a load cell to accurately record the applied load and four strain gauges,

affixed at the mid-height at each specimen in the configuration shown in Fig. 3. The strain

readings were used initially to verify that the load was being applied concentrically and later

to eliminate the effect of the elastic deformation of the plattens [12, 20, 22]. To verify

concentricity of loading, a small alignment load, approximately equal to 10% of the estimated

failure load was applied and the variation in strain around the cross-section was checked; in

all cases, individual strain gauge readings varied less than 5% from the average strain, which

was deemed acceptable. All data (load, voltage, strains and displacements) were recorded at

two seconds intervals using the data acquisition system DATASCAN.

Tests were continued beyond the ultimate load-carrying capacity of the stub columns, and the

post-ultimate response was recorded. The ultimate load and the corresponding end shortening

at ultimate load are given in Table 6, while the full load-end shortening curves for the tested

specimens are depicted in Fig. 4. Note that the reported end shortening curves and the end-

shortening values corresponding to ultimate load given in Table 6 refer to the true stub

column shortening, which is obtained on the basis of the recorded LVDT and strain readings

according to the procedure recommended in [22]. Failure was due to local buckling though

often after considerable plastic deformation; typical failure modes are depicted in Fig. 5.

2.4 Flexural buckling tests

Having established the basic material and cross-sectional response, twelve flexural buckling

tests were carried out in order to obtain ultimate load carrying capacity data and assess the

suitability of the current codified buckling curve for hollow sections [8] for lean duplex

stainless steel SHS and RHS. The tests were conducted on pin-ended columns with nominal

cross-sectional dimensions of 80×80×4, 60×60×3 and 80×40×4, in a similar fashion to the

tests described in [20]. Both minor and major axis buckling were considered for the RHS

80×40×4 specimens. The specimen lengths were chosen such that the buckling lengths (i.e.

total distance between knife edges) were equal to 800 mm, 1200 mm, 1600 mm and 2000

mm. This provided a range of non-dimensional member slendernesses, defined through by

Eq. (1), in accordance with Eurocode 3: Part 1.4 [8], from 0.57 to 2.02.

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cr2.0 NA (1)

where A is the cross-sectional area, σ0.2 is the 0.2% proof stress and Ncr is the elastic critical

buckling load of the column.

All tests were carried out in a 600 kN Instron capacity rig under displacement control. Knife

edges were employed to achieve the pin-ended boundary conditions, as shown in Fig. 6,

where the test rig is also depicted. A close-up of the knife edges is depicted in Fig. 7. The

employed instrumentation may also be seen in Fig. 6 and consisted of a load cell attached to

the top knife edge, two pairs of LVDTs at each end of the column measuring end rotations

and end shortening and two string pots attached at the mid-height of the columns measuring

the lateral deflection of the specimens.

Measurements of the specimen geometry, including initial global geometric imperfections e0

were conducted prior to testing and are reported in Table 7. The measured overall geometric

imperfections were generally small and hence the load was applied eccentrically at the ends

such that the combined effects of initial bow and loading eccentricity gave a total eccentricity

at mid-height of L/1500, where L is the pin-ended column buckling length. This value is the

statistical mean of geometric imperfections in steel structural members [23].

All columns failed by flexural buckling without any visible sign of local buckling. The full

load-lateral displacement curves were recorded and are shown in Figs. 8 and 9 for SHS and

RHS columns respectively. The key results from the column tests, including the ultimate load

and the lateral displacement at ultimate load are reported in Table 8. All obtained test results

have been used in the validation of the numerical models, as described in Section 3, and are

analysed and discussed in detail in Section 4 of the present paper.

3. Numerical modelling

3.1 Basic modelling assumptions

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The tests reported in the previous section have been utilised to validate FE models and

generate additional results by means of parametric studies, thus enabling a thorough

assessment of the key parameters affecting the structural response of lean duplex stainless

steel compression members. The general purpose finite element analysis package ABAQUS

[24] was used for all numerical studies reported in this paper. The FE simulations followed

the proposals regarding numerical modelling of stainless steel components reported in [25,

26].

Measured geometric properties reported in Tables 5 and 7 for stub columns and long columns,

respectively, have been employed in the FE models. Owing to the thin-walled nature of

tubular sections, and in line with similar previous investigations [7, 20, 25, 26, 27], shell

elements were employed to discretise the models. The 4-noded doubly curved shell element

with reduced integration S4R [24] has been utilised in this study. As discussed later, it was

assumed that the corner properties, as derived from the corner coupon tests, extended up to a

distance equal to two times the material thickness into the flat region of each face of the

models on either side of the corners. Two elements were utilised to discretise each of these

flat parts adjacent to the corners and hence, in order to maintain a uniform mesh size within

all flat parts of the models, an element size equal to the material thickness was required for all

models. A coarser, non-uniform mesh was shown to yield results of similar accuracy but

given the low computational cost associated with the finer mesh size, a uniform mesh was

employed. Regarding the root radii, three elements were used to discretise them, assuming

that their geometry is approximated by circular arcs.

Geometry, boundary conditions, applied loads and failure modes of the tested components

were observed to be symmetric. The displayed symmetry was exploited in the finite element

modelling with suitable boundary conditions applied along the symmetry axes, enabling

significant savings in computational time. Regarding the stub columns, only a quarter of the

section was modelled, whereas for the long columns, half of the cross-section was discretised.

For both stub columns and long columns the full component length was modelled. All degrees

of freedom were restrained at the end cross-sections of the stub column models, apart from

vertical translation at the loaded end, which was constrained via kinematic coupling to follow

the same vertical displacement. Similar boundary conditions were applied to the flexural

buckling models, with the only difference lying in the rotational degree of freedom about the

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axis of buckling of the end cross-sections, which was not restrained, thus enabling the

modelling of the pin-ended boundary conditions.

It has been experimentally verified that the cold-forming process induces strength

enhancements in the corner regions of cold-formed components for carbon steel [28] and

stainless steel [29]. The enhanced strength also extends beyond the curved corner regions into

the flat parts of the cross-section. A quantitative assessment of the effect of cold-forming on

the stress-strain response of lean duplex stainless steel can be found in [7]. Previous studies

[25, 26] suggest that the best agreement between experimental and FE results for cold-rolled

stainless steel hollow sections is obtained when the corner properties extend into the flat

regions by a distance equal to two times the material thickness. This has been verified by

experimental observations in the corner regions [29], and this approach has been followed in

the present study. The material properties derived from tensile corner tests (as reported in

Table 4) were assigned to the corner regions of the models and the adjacent flat regions up to

two times the material thickness, whereas compressive material properties (as reported in

Table 3) were assigned to the remainder of the sections.

Residual stresses in cold-formed tubular sections may be categorised as (1) bending residual

stresses that vary through the thickness of the sections and arise as a result of plastic

deformation during forming and (2) membrane residual stresses that are induced during the

seam-welding operation to complete the tube. Careful measurements [30] have shown the

latter to be relatively insignificant in stainless steel hollow sections and largely swamped by

the dominant bending residual stresses. Furthermore, the effect of the bending residual

stresses is inherently present in the material stress-strain properties [30, 31] since the residual

stresses that are released during the cutting of the coupons (causing longitudinal curvature)

are essentially reintroduced by straightening of the coupons during testing. Residual stresses

were not therefore explicitly introduced into the described models, but their influence was

present in the material modelling.

As mentioned in Section 2.1, a compound version [10-13] of the basic Ramberg-Osgood

material model [14, 15] was employed to simulate the stress-strain response of lean duplex

stainless steel, with the respective material parameters given in Tables 3-5. For incorporation

into the FE analyses, this material model was approximated with a multilinear curve, the

points of which were distributed proportionally to curvature of the original continuous curve

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[32], following a procedure described in [33], in order to minimise the error introduced by the

approximation. These points were thereafter converted into true stress true and log plastic

strain plln , as defined by Eqs. (2) and (3)

)1( nomnomtrue (2)

E)1ln( true

nomplln

(3)

where nom and nom are the engineering stress and strain respectively and E is the Young’s

modulus.

Based on the aforementioned modelling assumptions, a series of FE models were generated.

Linear eigenvalue buckling analyses using the subspace iteration method were initially

performed to extract the buckling mode shapes. These served as initial geometric

imperfection patterns used in the subsequent geometrically and materially non-linear

analyses. The modified Riks method [24], which is essentially a variation of the classical arc-

length method, was employed for the non-linear analyses to enable the full load-deflection

response, including into the post-ultimate range to be simulated.

The lowest local buckling mode shape was utilised to perturb the geometry of the stub

columns, while both the first local and first global mode shapes were introduced as geometric

imperfections in the flexural buckling models. Four variations of the local imperfection

amplitude were considered in the non-linear analyses; the maximum measured imperfection

reported in Table 5, 1/10 and 1/100 of the cross-sectional thickness and the imperfection

amplitude derived from the predictive model of [34] as adapted for stainless steels [25], given

by Eq. (4)

t023.0wcr

2.00

(4)

where σ0.2 is the tensile 0.2% proof stress given in Table 2 and σcr is the elastic critical

buckling stress of the most slender of the constituent plate element in the section, determined

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on the basis of the flat width of the element. For the global imperfection amplitudes, four

fractions of the respective buckling length were considered, namely L/500, L/1000, L/1500

and L/2000, noting that L/1500 represents the experimental imperfection.

3.2 Validation of models and parametric studies

In this section the results of the numerical simulations and the tests are compared, and the

sensitivity of the models to the key modelling parameters, particularly the imperfection

amplitudes, are examined. Comparisons with the test results are made to assess the accuracy

of the models and verify their suitability for performing parametric studies.

Table 9 presents the ratios of the numerical to experimental ultimate loads and corresponding

displacements at ultimate load for the varying imperfection amplitudes. The ultimate load is

generally well-predicted for the measured imperfection amplitude, the amplitude predicted by

the Dawson and Walker model (Eq. (4)) and t/100, whereas the use of the t/10 value results in

a clear underestimation of the load carrying capacity of the stub columns. The end shortening

at ultimate load appears to be more sensitive to the initial imperfection amplitude and is best

predicted when an imperfection amplitude from the Dawson and Walker model or t/100 is

used. The Dawson and Walker model predicts imperfection amplitudes on the basis of both

geometric and material properties of cross-sections. It has been shown, as in the current study,

to provide suitable local imperfections for inclusion in numerical models to accurately

simulate tests [25-27], and to provide a means of predicting measured imperfection

amplitudes directly [19, 25]. This model was therefore employed in the parametric studies

described in this paper to derive local imperfection amplitudes for both the stub columns and

long columns.

Overall excellent agreement between the experimental stub column results and those obtained

from the FE simulations was achieved; the compressive response was accurately predicted

throughout the full loading history, including initial stiffness, ultimate load, displacement at

ultimate load and post-ultimate response. Figs. 10 and 11 depict the experimental and

numerical load-end shortening curves using the imperfection amplitude predicted by the

Dawson and Walker model for the 80×40×4-SC2 and 80×80×4-SC2 stub columns, whereas a

comparison of experimental and numerical failure modes is displayed in Fig. 12.

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Good agreement between test and numerical results is also displayed for the flexural buckling

specimens. Comparisons are shown in Table 10, where it may be seen, as expected, that the

ratio of the numerically predicted ultimate buckling load to the experimental buckling load is

clearly influenced by the assumed initial global imperfection amplitude. The most accurate

and consistent prediction of test response is obtained for an imperfection amplitude of L/1500,

which coincides with the total imperfection amplitude (initial bow imperfection plus

eccentricity) present in the tests. Comparisons between experimental and FE results in terms

of load versus lateral deflection are depicted in Figs. 13, 14 and 15 for an SHS column, an

RHS column buckling about the major axis and an RHS column buckling about the minor

axis, respectively. The FE failure modes also compare well with the test failure modes, as

displayed in Fig. 16.

Upon validation of the FE models for both stub columns and long column parametric studies

have been conducted. The generated models adhere to the basic modelling assumptions stated

in Section 3.1. The material properties adopted in the FE parametric studies were based on the

averaged experimental material stress-strain curves; flat compressive and corner tensile

material properties were assigned to the respective parts of the models. Local geometric

imperfections in the form of the lowest buckling mode shape with an amplitude derived from

Eq. (4) were incorporated for both stub column and flexural buckling models, whereas the

global imperfection amplitude of the long columns was taken as L/1500.

All cross-sections considered in the parametric studies had an outer width B equal to 100 mm

and an outer height H equal to either 100 mm or 200 mm, thereby resulting into aspect ratios

of 1.0 and 2.0. The length of the stub column models was set equal to four times their mean

outer dimension, hence 400 mm for the SHS and 600 mm for the RHS models, while their

thickness varied from 1.6 mm to 13.0 mm to encompass a wide range of cross-sectional

slendernesses. The cross-section slenderness was defined as c/tε in accordance with Eurocode

3: Part 1-4 [8], where c is the flat element width, t is the element thickness and

)210000E)(f235( y . Regarding the flexural buckling models, constant thicknesses of

4.75 mm and 9.50 mm were selected for the 100×100 and 100×200 cross-sections

respectively, resulting in Class 3 cross-sections according to the slenderness limits given in

[8] - the actual c/tε ratio was 30, compared to the Class 3 slenderness limit of 30.7. The

buckling length of the columns was varied to cover a wide spectrum of member slendernesses

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ranging from 0.4 to 2.4. The results of the parametric studies are discussed in the following

section.

4. Analysis of results and design recommendations

4.1 Introduction

In this section, the applicability of the provisions of Eurocode 3: Part 1.4 [8], including the

Class 3 slenderness limit and effective width formula for internal elements in compression

and the buckling curve for hollow section columns to lean duplex stainless steel structural

components is assessed on the basis of both the experimental and numerical results reported

in this paper. Furthermore, the modified slenderness limits and effective width formulae for

stainless steel cross-sections, proposed by the authors on the basis of a significantly larger

experimental data pool than was available at the time of development of Eurocode 3: Part 1.4

in [9], are also assessed. Finally, comparisons of the structural performance of lean duplex

stainless steel with that of the more common stainless steel grades in construction are made.

In all code comparisons, the measured tensile material properties derived for each cross-

section from flat tensile coupon tests were utilised.

4.2 Class 3 slenderness limit for elements in compression

The obtained test and FE data were used to assess the applicability of the codified slenderness

limits to lean duplex stainless steel elements. For all experimental and numerical stub column

results, the ultimate load divided by the squash load, Fu/Aσ0.2, is plotted against the

slenderness of the most slender constituent element in the cross-section in Fig. 17, where the

respective Class 3 limits for carbon steel and stainless steel specified by Eurocode 3: Part 1.1

[35] and Eurocode 3: Part 1.4 [8], as well as the Class 3 limit proposed in [9] are also

included.

As shown in Fig. 17, the RHS (H/B=2.0) display superior load carrying capacity to their SHS

(H/B=1.0) counterparts of equal cross-sectional slenderness (i.e. c/tε). This is due to the

higher level of restraint offered by the narrow faces to the wider (more slender) faces of the

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RHS and the potential for stress redistribution once local buckling of the wider face plates

occurs. In order to maintain simplicity, the effect of element interaction on the cross-sectional

response is not accounted for in [8] or [35] and a conservative cross-section classification

approach is specified, according to which all elements are treated in isolation and the cross-

sectional response relates to its most slender element. More advanced approaches accounting

for element interaction have been derived for hot-rolled carbon steel H-sections [36], cold-

formed carbon steel sections [37] and cold-formed stainless steel sections [38].

Within the current cross-section classification approach codified in [8], the Class 3 limit (i.e.

the limit below which an element can be assumed to be fully effective) of 30.7ε is

conservative and could be relaxed to 37ε, as proposed by the authors [9] for other grades of

stainless steel. The respective carbon steel Class 3 limit of 42ε is marginally unconservative

and does not provide adequate reliability as assessed by the statistical analysis conducted in

[9], according to Annex D of EN 1990 [39].

4.3 Effective width formula

Slender (Class 4) cross-sections are treated in Eurocode 3: Part 1-4 [8] following the Von

Karman effective width approach, as modified according to experimental data of Winter [40-

42], to account for the occurrence of local buckling prior to reaching the 0.2% proof strength.

The effective width equation for internal elements given in Eurocode 3: Part 1.4 is compatible

with the corresponding codified Class 3 limit of 30.7ε, which has been shown to be rather

conservative. For consistency with the revised limit of 37ε, a revised effective width equation

was proposed [9], as given by Eq. (5):

1079.0772.0

2pp

(5)

where is the reduction factor for local buckling and p is the element slenderness, as

defined in [8]. The Class 3 limits set out in [8] and [9] and the Fu/Fy (ultimate load normalised

by the squash load) ratios predicted according to the respective effective width equations are

plotted together with the Fu/Fy data points derived from parametric studies against the c/tε

ratio of the most slender plate element in Fig. 18. The results confirm the adequacy but

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conservatism of the current Eurocode 3: Part 1.4 provisions and the applicability of the

proposed revised formula (Eq. (5)) [9].

4.4 Flexural buckling

The applicability of the buckling curve specified in Eurocode 3: Part 1.4 for hollow sections

to lean duplex stainless steel tubular columns is assessed by comparing the column test and

numerical data with the respective codified predictions. For both experimental and FE results,

the ultimate load has been normalised by the corresponding squash load (defined as Aσ0.2)

and plotted against the non-dimensional slenderness in Fig. 19, where the stub column test

data are also included. The effect of the aspect ratio is insignificant for slender columns, but

becomes increasingly important with decreasing member slenderness, because of the

increasing influence of cross-sectional behaviour (i.e. local buckling). Good agreement

between the test data and code predictions is observed and hence application of the current

buckling curve ( 4.00 and 49.0 ) to lean duplex stainless steel SHS and RHS columns

is proposed in the present paper.

4.5 Comparison of lean duplex with other stainless steel grades

The initial material cost of stainless steel comprises two components: the basic manufacturing

cost and the alloy adjustment factor, which depends on the alloying elements used and hence

varies markedly between grades. Lean duplex stainless steel only contains approximately

1.5% nickel, resulting in a relatively low alloy adjustment factor and hence a competitive

initial material cost [43]. In Figs. 20 and 21 the structural response of stub columns and long

columns of the most commonly adopted structural stainless steel grades (i.e. austenitic and

duplex grades) is compared with the corresponding lean duplex test data reported herein. The

stub column data included in Fig. 20 have been reported in [12, 44-49], whereas the flexural

buckling data were taken from [45-48, 50, 51]. In the determination of the slenderness

parameter plotted on the horizontal axis of Figs. 20 and 21, only geometric properties have

been included (c/t for stub columns and Lcr/i, where Lcr is the buckling length and i is the

radius of gyration, for long columns), so that the effect of material is accounted for only in the

vertical axis. In the high slenderness regime all stainless steel grades exhibit similar structural

capacities since failure is governed principally by stiffness. However, for stockier cross-

15

sections and members the lean duplex and conventional duplex structural components behave

similarly and exhibit superior performance to their austenitic counterparts of similar

geometric slenderness, since their higher strength can be fully utilized.

5. Conclusions

Eight stub column tests and twelve flexural buckling tests on lean duplex stainless steel SHS

and RHS have been reported in detail in the present paper. The results of the experimental

investigation were supplemented by numerically generated data. Upon validation of the FE

models, parametric studies were conducted to investigate the structural response over a wide

range of cross-sectional slenderness for the stub columns and member slenderness for the

long columns. Based on both experimental and numerical data, the provisions of Eurocode 3:

Part 1-4 for the classification and local buckling treatment of internal elements in

compression and buckling for stainless steel hollow section columns, were assessed. Both the

class 3 limit and the corresponding effective width equation for internal elements in

compression was shown to be adequate but conservative and the adoption of the more

favourable slenderness limits and effective width formulae [7] for stainless steel elements is

supported herein. Regarding the flexural buckling response of lean duplex stainless steel

columns, the current buckling curve for stainless steel hollow sections is deemed suitable.

Overall, lean duplex stainless steel is shown to offer superior structural performance

compared to the austenitic grades and at a lower cost [43], which represents a significant

economic advantage and renders lean duplex stainless steel an attractive choice for structural

applications.

Acknowledgements

The authors are grateful to Stalatube Finland for the supply of test specimens, to the UK

Outokumpu Stainless Steel Research Foundation for funding of the project and would like to

thank Stephanie Bouhala, Cheryl Parmar and Gordon Herbert for their contribution to the

experimental part of this research.

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References

[1] Gardner, L. (2005). The use of stainless steel in structures. Progress in Structural

Engineering and Materials. 7(2), 45-55.

[2] EN 10088-4. (2009) Stainless steels – Part 4: Technical delivery conditions for sheet/plate

and strip of corrosion resisting steels for general purposes. CEN.

[3] Gardner, L., Insausti, A., Ng, K. T. and Ashraf, M. (submitted). Elevated temperature

material properties of stainless steel alloys. Engineering Structures.

[4] Nilsson, J. O., Chai, G. and Kivisäkk, U. (2008). Recent development of stainless steels,

Proceedings of the Sixth European Stainless steel Conference, pp. 585-590, Finland.

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18

[20] Theofanous, M., Chan, T.M. and Gardner, L. (2009). Structural response of stainless

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[30] Cruise, R.B. and Gardner, L. (2008). Residual stress analysis of structural stainless steel

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1

Table 1: Chemical composition (% by weight) of test material

SectionC

(%)

Si

(%)

Mn

(%)

P

(%)

S

(%)

Cr

(%)

Ni

(%)

N

(%)

Mo

(%)

Cu

(%)

60×60×3 0.025 0.8 4.99 0.02 0.001 21.64 1.5 0.209 0.3 0.31

80×80×4 and 80×40×4

0.028 0.7 4.85 0.021 0.001 21.4 1.6 0.229 0.26 0.29

100×100×4 0.019 0.64 5.05 0.02 0.001 21.41 1.57 0.227 0.28 0.34

Table 2: Tensile flat material properties

Cross-sectionE

(N/mm2)σ0.2

(N/mm2)σ 1.0

(N/mm2)σ u

(N/mm2)εf

%

CompoundR-O coefficients

n n'0.2,1.0

SHS 100×100×4 198800 586 632 761 47 9.0 2.8

SHS 80×80×4 199900 679 736 773 42 6.5 4.2

SHS 60×60×3 209800 755 819 839 44 6.0 4.3

RHS 80×40×4 199500 734 785 817 50 10.1 3.4

Table

2

Table 3: Compressive flat material properties

Cross-section E (N/mm2) σ0.2 (N/mm2) σ1.0 (N/mm2) Compound R-O coefficients

n n'0.2,1.0

SHS 100×100×4 198200 560 642 8.3 2.6SHS 80×80×4 197200 657 770 4.7 2.6SHS 60×60×3 206400 711 845 5.0 2.7RHS 80×40×4 204000 607 734 4.6 2.9

Table 4: Tensile corner material properties

Cross-sectionE

(N/mm2)σ0.2

(N/mm2)σ 1.0

(N/mm2)σ u

(N/mm2)εf

%

CompoundR-O coefficients

n n'0.2,1.0

SHS 100×100×4 206000 811 912 917 32 6.3 4.1

SHS 80×80×4 210000 731 942 959 24 5.6 3.7

SHS 60×60×3 212400 885 1024 1026 22 6.3 4.0

RHS 80×40×4 213800 831 959 962 26 4.4 4.0

3

Table 5: Measured dimensions of stub columns

Specimen L (mm) B (mm) H (mm) t (mm) ri (mm) A (mm2) w0 (mm)

100×100×4-SC1 400.0 101.0 102.0 3.93 3.8 1495.2 0.071100×100×4- SC2 400.0 102.0 103.0 3.97 3.9 1524.7 0.07180×80×4- SC1 319.7 80.0 80.5 3.88 3.8 1147.4 0.08080×80×4- SC2 332.2 80.0 80.0 3.81 3.6 1125.0 0.08060×60×3- SC1 239.8 60.0 60.0 3.09 2.3 683.0 0.06260×60×3- SC2 240.0 60.0 60.0 3.17 2.1 700.4 0.06280×40×4- SC1 239.9 39.0 79.5 3.76 3.5 799.8 0.05880×40×4- SC2 237.8 39.6 79.5 3.81 4.3 808.8 0.058

Table 6: Summary of test results for stub columns.

Specimen Ultimate Load Fu (kN) End shortening at ultimate load δu (mm)

100×100×4-SC1 1022 3.63100×100×4- SC2 1037 4.01

80×80×4- SC1 923 4.13

80×80×4- SC2 915 3.88

60×60×3- SC1 613 4.09

60×60×3- SC2 616 3.69

80×40×4- SC1 709 4.33

80×40×4- SC2 710 4.12

4

Table 7: Measured geometric properties of columns

SpecimenAxis of

bucklingH (mm) B (mm) t (mm)

ri

(mm)A (mm2)

Buckling length

Lcr (mm)

Global imperfection

amplitude e0 (mm)80×80×4-2000 - 79.6 79.5 3.80 3.4 1116.7 1999.0 0.4180×80×4-1200 - 79.3 79.6 3.72 3.8 1091.0 1199.5 0.1060×60×3-2000 - 60.0 60.0 3.13 2.7 689.1 1999.0 0.3160×60×3-1600 - 59.6 60.0 3.15 2.4 692.4 1599.0 0.3260×60×3-1200 - 60.0 60.0 3.13 2.4 689.8 1199.0 0.2660×60×3-800 - 60.0 60.0 3.13 2.4 690.8 799.0 0.2380×40×4-MI-1600 Minor 39.0 79.2 3.80 4.3 800.4 1600.0 0.0380×40×4-MJ-1600 Major 79.5 39.3 3.95 4.0 835.8 1599.5 0.2580×40×4-MI-1200 Minor 40.0 79.2 3.80 3.8 811.3 1199.0 0.1580×40×4-MJ-1200 Major 79.6 39.5 3.96 3.6 842.4 1199.5 0.1380×40×4-MI-800 Minor 39.5 79.4 3.80 3.6 810.0 797.2 0.2280×40×4-MJ-800 Major 79.9 39.5 3.93 4.1 835.6 799.0 0.28

Table 8: Key results from flexural buckling tests

Specimen Non-dimensional slenderness Ultimate load Fu (kN) Lateral deflection at Fu (mm)

80×80×4-2000 1.21 361.9 20.080×80×4-1200 0.73 672.5 4.760×60×3-2000 1.66 162.3 19.560×60×3-1600 1.34 231.7 15.460×60×3-1200 0.99 326.9 10.460×60×3-800 0.66 445.9 5.980×40×4-MI-1600 2.02 160.4 4.180×40×4-MJ-1600 1.14 406.3 3.880×40×4-MI-1200 1.47 237.4 9.980×40×4-MJ-1200 0.86 497.7 7.780×40×4-MI-800 0.99 366.6 9.080×40×4-MJ-800 0.57 546.2 6.3

5

Table 9 Comparison of the stub column test results with FE results for varying imperfection amplitudes

Stub columndesignation

Measured amplitude w0

t/10 t/100Dawson and

Walker model

FE Fu/Test Fu

FE δu /Test δu

FE Fu/Test Fu

FE δu /Test δu

FE Fu/Test Fu

FE δu /Test δu

FE Fu/Test Fu

FE δu /Test δu

100×100×4-SC1 0.95 0.71 0.86 0.61 0.98 0.78 0.97 0.73

100×100×4- SC2 0.96 0.64 0.87 0.50 0.98 0.70 0.98 0.69

80×80×4- SC1 1.00 0.68 0.92 0.45 1.01 0.75 1.02 0.80

80×80×4- SC2 1.02 0.81 0.95 0.57 1.05 0.96 1.06 0.98

60×60×3- SC1 0.97 0.86 0.90 0.54 0.98 0.91 0.98 0.91

60×60×3- SC2 0.99 0.89 0.93 0.57 1.00 0.99 1.00 1.02

80×40×4- SC1 1.00 0.83 0.90 0.55 1.03 0.93 1.03 0.93

80×40×4- SC2 0.97 0.76 0.89 0.61 1.01 1.03 1.01 1.04

Mean 0.98 0.77 0.90 0.55 1.00 0.88 1.01 0.89

COV 0.02 0.12 0.03 0.10 0.03 0.14 0.03 0.15

6

Table 10 Comparison of the column test results with FE results for varying imperfection amplitudes

SpecimenFE Fu/ Test Fu

L/500 L/1000 L/1500 L/2000

80×80×4-2000 0.96 1.03 1.06 1.08

80×80×4-1200 0.89 0.94 0.95 0.96

60×60×3-2000 0.94 1.00 1.03 1.04

60×60×3-1600 0.93 0.99 1.02 1.04

60×60×3-1200 0.94 1.00 1.03 1.04

60×60×3-800 0.99 1.01 1.02 1.03

80×40×4-MI-1600 0.81 0.87 0.89 0.90

80×40×4-MJ-1600 0.85 0.90 0.93 0.94

80×40×4-MI-1200 0.87 0.93 0.96 0.97

80×40×4-MJ-1200 0.90 0.94 0.96 0.98

80×40×4-MI-800 0.92 0.97 0.99 1.00

80×40×4-MJ-800 1.01 1.05 1.07 1.08

Mean 0.92 0.97 0.99 1.01

COV 0.06 0.06 0.05 0.05

1

Fig. 1: Lean duplex stainless steel footbridge in Siena, Italy.

Figure

2

Fig. 2: Section labelling convention and location of flat and corner coupons.

ri

Weld

Corner coupon

t

B

H y y

z

z

Flat coupon

3

Fig. 3: Stub column testing apparatus.

4

0

400

800

1200

0 2 4 6 8 10 12End shortening (mm)

Loa

d (k

N) 80×80×4-SC2

80×80×4-SC1

60×60×3-SC260×60×3-SC1

100×100×4-SC2

100×100×4-SC1

80×40×4-SC2

80×40×4-SC1

Fig. 4: Load-end shortening curves for stub columns.

5

Fig. 5: Typical stub column failure modes (from left to right: 60×60×3-SC1, 80×80×4-SC1, 80×40×4-SC1).

6

Fig. 6: Test setup for flexural buckling tests.

LVDTs to measure end rotation

Knife edges

String pots to measure lateral deflection

Column

7

Fig. 7: Knife edge detail.

8

0

200

400

600

800

0 10 20 30 40 50Lateral deflection (mm)

Loa

d (k

N)

80×80×4-1200

60×60×3-800

80×80×4-2000

60×60×3-1200

60×60×3-1600

60×60×3-2000

Fig. 8: Load-lateral displacement curves for SHS columns.

9

0

150

300

450

600

0 5 10 15 20 25 30 35 40

Lateral deflection (mm)

Loa

d (k

N)

80×40×4-MJ -800

80×40×4-MI -800

80×40×4-MI -1600

80×40×4-MJ -1200

80×40×4-MJ -1600

80×40×4-MI -1200

Fig. 9: Load-lateral displacement curves for RHS columns.

10

0

300

600

900

0 2 4 6 8 10

End shortening (mm)

Loa

d (k

N)

Test

FE

Fig. 10: Experimental and numerical load-end shortening curves for 80×40×4-SC2.

11

0

400

800

1200

0 2 4 6 8

End shortening (mm)

Loa

d (k

N)

Test

FE

Fig. 11: Experimental and numerical load-end shortening curves for 80×80×4-SC2.

12

Fig. 12: Experimental and FE failure modes for SHS 80×80×4-SC2.

13

0

50

100

150

200

0 10 20 30 40 50

Lateral deflection (mm)

Loa

d (k

N)

Test

FE

Fig. 13: Experimental and numerical load-lateral displacement cures for SHS60×60×3-L=2000 mm column.

14

0

150

300

450

600

0 5 10 15 20 25 30

Lateral deflection (mm)

Loa

d (k

N)

Test

FE

Fig. 14: Experimental and numerical load-lateral displacement cures for 80×80×4-MJ-L=1200 mm column.

15

0

100

200

300

0 5 10 15 20 25 30

Lateral deflection (mm)

Loa

d (k

N)

Test

FE

Fig. 15: Experimental and numerical load-lateral displacement cures for 80×80×4-MI-L=1200 mm column.

16

Fig. 16: Experimental and FE failure modes for SHS 80×80×4-L=1600 mm column.

17

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 10 20 30 40 50 60 70 80 90 100 110

c/tε

Fu/

Fy

FE-aspect ratio 1.0FE-aspect ratio 2.0Test results-aspect ratio 1.0Test results-aspect ratio 2.0

EC3: Part 1-4 Class 3 limit

EC3: Part 1-1 Class 3 limit

Gardner and Theofanous Class 3 limit [9]

Fig. 17: Current and proposed Class 3 slenderness limit for internal elements in compression.

18

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 10 20 30 40 50 60 70 80 90 100 110

c/tε

Fu/

Fy

FE-aspect ratio 1.0

FE-aspect ratio 2.0

EC3: Part1.4-aspect ratio 1.0

EC3: Part1.4-aspect ratio 2.0

Proposed [9]-aspect ratio 1.0

Proposed [9]-aspect ratio 2.0

EC3: Part 1-4 Class 3 limit

Gardner and Theofanous Class 3 limit [9]

Fig. 18: Assessment of EC3: Part 1.4 and proposed effective width formulae for internal elements.

19

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.0 0.5 1.0 1.5 2.0 2.5

Fu/

Fy

FE-SHSFE-RHS-MAFE-RHS-MITest-SHSTest-RHS-MATest-RHS-MITest stub columns

EC3 buckling curve

Fig. 19: Normalised test and FE column results and assessment of EC3 buckling curve.

20

0

250

500

750

1000

0 20 40 60 80c/t

Fu/

A (

N/m

m2 )

Lean DuplexAusteniticDuplex

Fig. 20: Performance of stub columns of various stainless steel grades.

21

0

200

400

600

800

1000

0 20 40 60 80 100 120

Geometric slenderness (Lcr/i)

Fu/

A (

N/m

m2 )

Lean Duplex

Austenitic

Duplex

Fig. 21: Performance of columns of various stainless steel grades.